What is an SAD? Shoulder anterior dislocation/ subacromial decompression (SAD)? Please try not to use abbreviations in the first posting.

I can't be totally sure that the head deviation, which is possible, during the surgery caused the issue. It could be any number of things. However considering it is one would propose to get your physio to investigate the upper cervical spine, especially C2/3. Mobilisation through range may well resolve the paresthesia within one session if that is the cause.